Supersymmetric M-theory compactifications with fluxes on seven-manifolds and G-structures

TL;DR

This work develops a systematic framework for supersymmetric M-theory compactifications on seven-manifolds with background fluxes by leveraging $G$-structure technology. By relating the four-form flux components to the intrinsic torsion of the internal manifold, the authors derive necessary SUSY conditions that constrain both geometry and flux, and they show that the presence of two nowhere-vanishing vectors on a seven-manifold naturally yields an $SU(3)$ structure for ${\cal N}=1$ and can be extended to an $SU(2)$ structure to accommodate ${\cal N}=2$ vacua. The analysis identifies the primitive $G_{27}$ component as central to warped solutions and provides explicit representations of the torsion in terms of warp-factor and flux data. This work thereby lays out a pathway toward a geometric classification of M-theory flux vacua via intrinsic torsion and clarifies when and how higher supersymmetry may emerge from flux and geometry.

Abstract

We consider Minkowski compactifications of M-theory on generic seven-dimensional manifolds. After analyzing the conditions on the four-form flux, we establish a set of relations between the components of the intrinsic torsion of the internal manifold and the components of the four-form flux needed for preserving supersymmetry. The existence of two nowhere vanishing vectors on any seven-manifold with G_2 structure plays a crucial role in our analysis, leading to the possibility of four-dimensional compactifications with N=1 and N=2 supersymmetry.